Types of angles
Classify angles as acute, right, obtuse, straight or reflex, and use angle relationships to find missing angles.
Worked examples
Classifying an angle
Straightforward
Problem
An angle measures . Classify this angle.
1
Recall the angle classifications.
Acute: \quad Right: \quad Obtuse: \quad Straight: \quad Reflex:
2
Compare to the ranges.
3
State the classification.
is an obtuse angle.
Answer
Obtuse angle
Finding a missing supplementary angle
Moderate
Problem
Two angles are supplementary and one of them is . Find the other angle.
1
Recall that supplementary angles add to .
2
Substitute the known angle.
3
Solve for the unknown angle.
Answer
Finding an unknown angle on a straight line
Challenging
Problem
Two angles on a straight line are and . Find the value of .
1
Recall that angles on a straight line add to .
2
Simplify the left side.
3
Solve for .
, so
Answer
Practise
Q1·Straightforward
An angle measures . What type of angle is this?
Explanation
is between and , so it is an acute angle.
Q2·Straightforward
An angle measures . What type of angle is this?
Explanation
is exactly a right angle.
Q3·Straightforward
An angle measures . What type of angle is this?
Explanation
is between and , so it is an obtuse angle.
Q4·Straightforward
An angle measures . What type of angle is this?
Explanation
is between and , so it is a reflex angle.
Q5·Moderate
Two angles are supplementary. One angle is . Find the other angle in degrees.
Explanation
Q6·Moderate
Two angles are complementary. One angle is . Find the other angle in degrees.
Explanation
Q7·Moderate
Two straight lines intersect at a point. One of the angles formed is . Find the size of the vertically opposite angle in degrees.
Explanation
Vertically opposite angles are equal, so the angle is also .
Q8·Moderate
Four angles meet at a point. Three of the angles are , and . Find the fourth angle .
Explanation
Q9·Challenging
Three angles on a straight line are , and . Find the value of .
Explanation
, so and .
Q10·Challenging
Two straight lines intersect. One angle is and the vertically opposite angle is . Find the value of .
Explanation
, so and .
Q11·Challenging
Two supplementary angles are in the ratio . Find the size of the larger angle in degrees.
Explanation
, so . The larger angle is .
Q12·Challenging
Three angles on a straight line are , and . Find the value of .
Explanation
, so , giving and .